Question: Divide the following complex numbers. $ \dfrac{12-12i}{-3i}$
Solution: Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{12-12i}{-3i} = \dfrac{12}{-3i} - \dfrac{12i}{-3i}$ Factor out a $1/i$ $\dfrac{12}{-3i} - \dfrac{12i}{-3i} = \dfrac 1i \left( \dfrac{12}{-3} - \dfrac{12i}{-3} \right) = \dfrac 1i (-4+4i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (-4+4i) = -i (-4+4i) = 4i - 4i^2 = 4+4i$